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The Strong Decay Patterns of the $1^{-+}$ Exotic Hybrid Mesons

We calculate the coupling constants of the decay modes $1^{-+}\rightarrowρπ, f_1π, b_1π, ηπ, η'π, a_1π, f_1η$ within the framework of the light-cone QCD sum rule. Then we calculate the partial width of these decay channels, which differ greatly from the existing calculations using phenomenological models. For the isovector $1^{-+}$ state, the dominant decay modes are $ρπ, f_1π$. For its isoscalar partner, its dominant decay mode is $a_1π$. We also discuss the possible search of the $1^{-+}$ state at BESIII, for example through the decay chains $J/ψ(ψ')\to π_1 +γ$ or $J/ψ(ψ')\to π_1 +ρ$ where $π_1$ can be reconstructed through the decay modes $π_1\to ρπ\to π^+π^-π^0$ or $π_1\to f_1(1285)π^0$. Hopefully the present work will be helpful to the experimental establishment of the $1^{-+}$ hybrid meson.